Polyimide resins, compositions, polyimide films, optical materials, cladding materials, and optical waveguides for low refractive index materials, as well as polyamic acids and compositions for low refractive index materials.

Abstract

To provide a polyimide resin for low refractive index materials that achieves both a low refractive index and a low coefficient of thermal expansion. [Solution] A polyimide resin comprising an acid anhydride and a diamine, wherein (1) the acid anhydride is a tetracarboxylic dianhydride having a substituent with a fluorine atom and an aromatic ring structure which may also be a condensed structure, and the diamine is a diamine with an aromatic ring or biphenyl skeleton which may also be a condensed structure, or (2) the acid anhydride is an alicyclic tetracarboxylic dianhydride and the diamine is a diamine with an aromatic ring or biphenyl skeleton which may also be a condensed structure.

Description

[Technical Field]

[0001] This disclosure relates to polyimide resins, compositions, polyimide films, optical materials, cladding materials, and optical waveguides for low refractive index materials, as well as polyamic acids and compositions for low refractive index materials. [Background technology]

[0002] In the field of optics, plastic materials such as polyimide resins, epoxy resins, and acrylate resins are widely used. However, compared to metal materials, resins generally have a larger coefficient of linear thermal expansion, leading to the problem of substrate warping due to heating after lamination. Furthermore, a low refractive index and a low coefficient of linear thermal expansion are generally in a trade-off relationship, making it difficult to achieve both simultaneously. To date, resin compositions have been reported that are excellent in transparency and low refractive index, and have low thermal expansion, and that contain (A) an epoxy compound having two or more epoxy groups, (B) a compound having a phenolic hydroxyl group, (C) silica particles with an average particle size of 1 nm or more and 70 nm or less, and (D) silicone oil (see, for example, Patent Document 1). [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2016-180014 [Overview of the project] [Problems that the invention aims to solve]

[0004] The present disclosure aims to provide a polyimide resin for low refractive index materials that achieves both a low refractive index and a low coefficient of thermal expansion. [Means for solving the problem]

[0005] <1> It consists of an acid anhydride and a diamine, The acid anhydride is at least one selected from the group consisting of a compound represented by the following general formula (A-1a) and a compound represented by the following general formula (A-1b), The diamine is at least one selected from the group consisting of a compound represented by the following general formula (B-1) and a compound represented by the following general formula (B-2), and it is a polyimide resin for a low refractive index material. [Chemical formula] In the general formula (A-1a), R is each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocyclic ring which may have a substituent, at least one R 1 has a fluorine atom, m represents an integer of 0 to 3. [Chemical formula] In the general formula (A-1b), R 1 is each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocyclic ring which may have a substituent, n represents an integer of 1 to 5, R 2 is each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocyclic ring which may have a substituent, and two adjacent R 2 may be bonded to each other to form a cycloalkyl group, at least one R 2 is a fluoroalkyl group which may have a substituent, X is each independently selected from the group consisting of -O-, -C(R 3 )2-, and -SO2-, R 3 is each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocyclic ring which may have a substituent, and two adjacent R 3These may bond to each other to form a cycloalkyl group. [ka] In the general formula (B-1), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. m represents an integer between 0 and 3. n represents an integer from 0 to 5. o represents an integer from 0 to the maximum number of substituents. R 2 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 2 These may bond to each other to form a cycloalkyl group. at least one R 2 This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-, R 3 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. [ka] In the general formula (B-2), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R 1 It has a fluorine atom, Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and the maximum number of substituents. <2> The above general formula (B-1) is either the following general formula (B-1a) or the following general formula (B-1b), The above general formula (B-2) is the following general formula (B-2a) <1> This is the polyimide resin described in [reference]. [ka] In the general formula (B-1a), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. 'o' represents an integer between 0 and 4. [ka] In the general formula (B-1b), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. m represents an integer between 1 and 3. 'o' represents an integer between 0 and the maximum number of substituents. [ka] In the general formula (B-2a), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R 1 It has a fluorine atom, 'o' represents an integer between 0 and 8. <3> It consists of an acid anhydride and a diamine, The acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formulas (A-2a) to (A-2g). The polyimide resin for low refractive index materials is one or more diamines selected from the group consisting of compounds represented by the following general formula (B-3) and compounds represented by the following general formula (B-4). [ka] In the general formulas (A-2a) to (A-2g), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. R 2 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. [ka] In the general formula (B-3), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. m represents an integer between 0 and 3. n represents an integer from 0 to 5. o represents an integer from 0 to the maximum number of substituents. R 2 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R 2 This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-, R 3Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. [ka] In the general formula (B-4), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and the maximum number of substituents. <4> The above general formula (B-3) is either the following general formula (B-3a) or the following general formula (B-3b), The above general formula (B-4) is the following general formula (B-4a) <3> This is the polyimide resin described in [reference]. [ka] In the general formula (B-3a), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. 'o' represents an integer between 0 and 4. [ka] In the general formula (B-3b), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. m represents an integer between 1 and 3. 'o' represents an integer between 0 and the maximum number of substituents. [ka] In the general formula (B-4a), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R 1 It has a fluorine atom, 'o' represents an integer between 0 and 8. <5> The refractive index is 1.57 or less. The coefficient of linear expansion is 50 ppm / K or less, <1> from <4> It is a polyimide resin as described in any one of the items. <6> A polyimide resin having the structural unit of the following general formula (1), [ka] In the above general formula (1), R1 is R a The (CO)4 portion represents a tetravalent group derived from a tetravalent tetracarboxylic acid with 2 or more carbon atoms, R b The (N)2 portion represents a tetravalent group derived from a divalent diamine with 2 or more carbon atoms. The free volume fraction and average number of neighboring atoms of the amorphous polyimide resin in equilibrium at a temperature of 300K and a pressure of 1atm, as calculated by molecular dynamics calculations, satisfy either of the following conditions (1) or (2): (1) The free volume fraction is 0.23 to 0.32, and the average number of neighboring atoms is 3.90 to 4.60. (2) The free volume fraction is 0.23 to 0.32, the average number of neighboring atoms is 3.90 to 4.60, and it does not contain a trifluoromethyl group. (3) The free volume fraction is 0.24 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not contain a trifluoromethyl group. (4) The free volume fraction is 0.28 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not contain a trifluoromethyl group. The average number of neighboring atoms is the average number of neighboring atoms per number of atoms constituting the molecular dynamics calculation system, The polyimide resin for low refractive index materials is such that the number of adjacent atoms is the total number of atom pairs satisfying both (a) and (b) below. (a) Atomic pairs that share one side of a Voronoi cell, with each atom acting as a parent point. (b) Atomic pairs separated by four or more bonds, or atomic pairs between different molecules <7> The free volume fraction and average number of neighboring atoms of the amorphous polyimide resin in equilibrium at a temperature of 300K and a pressure of 1atm, as calculated by molecular dynamics calculations, satisfy either of the following conditions (1) or (2): (1) The free volume fraction is 0.23 to 0.32, and the average number of neighboring atoms is 3.90 to 4.60. (2) The free volume fraction is 0.23 to 0.32, the average number of neighboring atoms is 3.90 to 4.60, and it does not contain a trifluoromethyl group. (3) The free volume fraction is 0.24 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not contain a trifluoromethyl group. (4) The free volume fraction is 0.28 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not contain a trifluoromethyl group. The average number of neighboring atoms is the average number of neighboring atoms per number of atoms constituting the molecular dynamics calculation system, The number of adjacent atoms is the total number of atom pairs that satisfy both (a) and (b) below, <1> from <5> It is a polyimide resin as described in any one of the items. (a) Atomic pairs that share one side of a Voronoi cell, with each atom acting as a parent point. (b) Atomic pairs separated by four or more bonds, or atomic pairs between different molecules <8> The aforementioned <1> from <7> This is a composition for low refractive index materials containing a polyimide resin as described in any one of the above. <9> The aforementioned <1> from <7> This is a polyimide film for low refractive index materials containing the polyimide resin described in any one of the items. <10> The aforementioned <1> from <7> This optical material contains a polyimide resin as described in any one of the items. <11> The aforementioned <1> from <7> This is a clad material containing the polyimide resin described in any one of the items. <12> The aforementioned <11> This is an optical waveguide having the cladding material described above. <13> It consists of an acid anhydride and a diamine, The acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formula (A-1a) and compounds represented by the following general formula (A-1b). The diamine is a polyamic acid for low refractive index materials, wherein the diamine is one or more compounds selected from the group consisting of compounds represented by the following general formula (B-1) and compounds represented by the following general formula (B-2). [ka] In the above general formula (A-1a), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R 1 It has a fluorine atom, m represents an integer between 0 and 3. [ka] In the general formula (A-1b), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. n represents an integer from 1 to 5. R 2 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 2 These may bond to each other to form a cycloalkyl group. at least one R 2 This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R 3Selected from the group consisting of )2- and -SO2-, R 3 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. [ka] In the general formula (B-1), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. m represents an integer between 0 and 3. n represents an integer from 0 to 5. o represents an integer from 0 to the maximum number of substituents. R 2 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 2 These may bond to each other to form a cycloalkyl group. at least one R 2 This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-, R 3 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. [ka] In the general formula (B-2), R 1Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R 1 It has a fluorine atom, Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and the maximum number of substituents. <14> It consists of an acid anhydride and a diamine, The acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formulas (A-2a) to (A-2g). The diamine is a polyamic acid for low refractive index materials, wherein the diamine is one or more compounds selected from the group consisting of compounds represented by the following general formula (B-3) and compounds represented by the following general formula (B-4). [ka] In the general formulas (A-2a) to (A-2g), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. R 2 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. [ka] In the general formula (B-3), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. m represents an integer between 0 and 3. n represents an integer from 0 to 5. o represents an integer from 0 to the maximum number of substituents. R 2 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R 2 This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-, R 3 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. [ka] In the general formula (B-4), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and the maximum number of substituents. <15> The aforementioned <13> or <14> This is a composition for low refractive index materials containing the polyamic acid and solvent described above. [Effects of the Invention]

[0006] According to this disclosure, it is possible to provide a polyimide resin for low refractive index materials that achieves both a low refractive index and a low coefficient of thermal expansion. [Brief explanation of the drawing]

[0007] [Figure 1] Figure 1 is a cross-sectional view showing an example of an optical waveguide according to this embodiment. [Figure 2] Figure 2 is a cross-sectional view showing another example of the optical waveguide in this embodiment. [Figure 3] Figure 3 is a graph showing the relationship between refractive index, free volume fraction, and average number of neighboring atoms in the molecular dynamics simulation of the example. [Figure 4] Figure 4 is a graph showing the relationship between the coefficient of linear expansion, the free volume fraction, and the average number of neighboring atoms in the molecular dynamics simulation of the example. [Figure 5] Figure 5 is a graph showing the relationship between experimental values ​​and calculated values ​​from molecular dynamics simulations for refractive index. [Figure 6] Figure 6 is a graph showing the relationship between experimental values ​​and calculated values ​​from molecular dynamics simulations for the coefficient of thermal expansion. [Modes for carrying out the invention]

[0008] (Polyimide resin for low refractive index materials) The polyimide resin for low refractive index materials of this disclosure is a polyimide resin used in applications of low refractive index materials that achieves both a low refractive index and a low coefficient of thermal expansion, and is a polyimide resin that (1) has a specific chemical structure in the first embodiment, (2) has a specific chemical structure in the second embodiment, (3) satisfies the requirements for free volume fraction and average number of neighboring atoms in the third embodiment, or (4) satisfies (1) or (2) and (3) above. The polyimide resin preferably has a refractive index of 1.57 or less and a coefficient of thermal expansion of 50 ppm / K or less.

[0009] The polyimide resin for low refractive index materials described herein is based on the following findings made by the inventors. In other words, conventionally, a low refractive index and a low coefficient of thermal expansion are generally in a trade-off relationship, making it difficult to achieve both. However, as shown in the examples described later, the inventors identified two parameters, "free volume fraction" and the newly defined "average number of neighboring atoms," through molecular dynamics simulations using an amorphous polyimide resin, and found that these two parameters correlate with the calculated values ​​of refractive index and coefficient of thermal expansion. In addition, as a result of evaluating the relationship between the refractive index and the experimental values ​​of the coefficient of thermal expansion for numerous known polyimide resins, they found that a high "free volume fraction" contributes to a low refractive index and a low coefficient of thermal expansion, and that a low "average number of neighboring atoms" contributes to a low refractive index. From this, we found that a polyimide resin that achieves both a low refractive index and a low coefficient of thermal expansion can be identified using the free volume fraction and the average number of neighboring atoms as indicators. Furthermore, we identified the chemical structure of a polyimide resin that achieves both a low refractive index and a low coefficient of thermal expansion through molecular dynamics simulations.

[0010] [First Embodiment] The polyimide resin for low refractive index materials in the first embodiment of this disclosure is a polyimide resin comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more selected from the group consisting of compounds represented by the following general formula (A-1a) and compounds represented by the following general formula (A-1b), and the diamine is one or more selected from the group consisting of compounds represented by the following general formula (B-1) and compounds represented by the following general formula (B-2).

[0011] <Acid anhydride> The aforementioned acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formula (A-1a) and compounds represented by the following general formula (A-1b). The aforementioned acid anhydride may be used alone or in combination of two or more types.

[0012] [ka]

[0013] In the above general formula (A-1a), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and at least one R 1 It contains a fluorine atom.

[0014] The substituent can be any group having a structure that can be substituted on the target, but examples include one or more selected from the group consisting of halogens, hydroxyl groups, alkoxy groups, alkylcarbonyl groups, alkylcarbonyloxy groups, alkoxycarbonyl groups, arylcarbonyloxy groups, aryloxycarbonyl groups, and aryl groups. The number of substituents can be selected from an integer within the range of one to the maximum number of substituents that can be substituted (hereinafter referred to as the "maximum number of substituents") (for example, one, two, three, etc.).

[0015] The aforementioned R 1 Preferably, each of these is independently selected from the group consisting of hydrogen, fluorine, C1-C4 alkyl groups, and C1-C4 fluoroalkyl groups, and more preferably selected from the group consisting of hydrogen, fluorine, methyl group (-CH3), and trifluoromethyl group (-CF3). at least one R 1 It has a fluorine atom, and one of the R 1 is fluorine, and the other R 1 However, each is preferably independently selected from the group consisting of hydrogen, fluorine, C1-C4 alkyl groups, and C1-C4 fluoroalkyl groups; one of the R 1 is fluorine, and the other R 1 However, it is more preferable that each is independently selected from the group consisting of hydrogen, fluorine, a methyl group, and a trifluoromethyl group.

[0016] In the general formula (A-1a) above, m represents an integer from 0 to 3, and is preferably 0, 1, or 2, and more preferably 0 or 1.

[0017] [ka]

[0018] In the general formula (A-1b), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. R in the above general formula (A-1b) 1 The substituent in is R of the general formula (A-1a) 1 The substituents described in the above can be selected as appropriate. The aforementioned R 1 Preferably, each of these is independently selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0019] In the general formula (A-1b) above, n represents an integer from 1 to 5, preferably an integer from 1 to 3, and more preferably 1.

[0020] In the general formula (A-1b), R 2 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 2 These may bond to each other to form a cycloalkyl group, and at least one R 2 This is a fluoroalkyl group which may have substituents. R in the above general formula (A-1b) 2 The substituent in is R of the general formula (A-1a) 1 The substituents described in the above can be selected as appropriate. One of the R 2 is a fluoroalkyl group having 1 to 4 carbon atoms, and the other R 2 However, each is preferably independently selected from the group consisting of hydrogen, an alkyl group having 1 to 4 carbon atoms, and an aromatic ring; one of the R1 is a trifluoromethyl group, and the other R 1 is more preferably each independently selected from the group consisting of hydrogen, a methyl group, a trifluoromethyl group, and a phenyl group.

[0021] In the general formula (A-1b), X is each independently selected from the group consisting of -O-, -C(R 3 )2-, and -SO2-.

[0022] In the general formula (A-1b), R 3 is each independently selected from the group consisting of hydrogen, a halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocyclic ring which may have a substituent, and two adjacent R 3 may be bonded to each other to form a cycloalkyl group. As the substituent in R 3 in the general formula (A-1b), the matters described as the substituent in R 1 in the general formula (A-1a) can be appropriately selected. As R 3 it is more preferably each independently selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0023] <Diamine> The diamine is one or more selected from the group consisting of a compound represented by the following general formula (B-1) and a compound represented by the following general formula (B-2). In one embodiment, it is preferable that the general formula (B-1) is any one of the following general formula (B-1a) and the following general formula (B-1b), and it is preferable that the general formula (B-2) is the following general formula (B-2a). The diamine may be used alone or in combination of two or more.

[0024]

Chemical formula

[0025] In the general formula (B-1), R 1 is each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocyclic ring which may have a substituent. As the substituent in R of the general formula (B-1) 1 the matters described as the substituent in R of the general formula (A-1a) 1 can be appropriately selected. As R 1 it is preferably each independently selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0026] In the general formula (B-1), l represents an integer of 1 to 3, preferably 1 or 2, and more preferably 1. m represents an integer of 0 to 3, preferably 0, 1 or 2, and more preferably 0 or 1. n represents an integer of 0 to 5, preferably an integer of 0 to 3, and more preferably 0 or 1. o represents an integer of 0 to the maximum number of substituents, preferably an integer of ≥ 25% of the maximum number of substituents, and more preferably an integer of ≥ 50% of the maximum number of substituents.

[0027] In the general formula (B-1), R 2 is each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocyclic ring which may have a substituent, and two adjacent Rs 2 may be bonded to each other to form a cycloalkyl group, and at least one R 2 is a fluoroalkyl group which may have a substituent. As the substituent in R of the general formula (B-1) 2 the matters described as the substituent in R of the general formula (A-1a) 1The substituents described can be appropriately selected, but halogens other than fluorocarbons and alkyl groups having 1 to 4 carbon atoms are preferred. One of the R 2 is a fluoroalkyl group having 1 to 4 carbon atoms, and the other R 2 However, each is preferably independently selected from the group consisting of hydrogen, an alkyl group having 1 to 4 carbon atoms, and an aromatic ring; one of the R 1 is a trifluoromethyl group, and the other R 1 However, it is more preferable that each is independently selected from the group consisting of hydrogen, a methyl group, a trifluoromethyl group, and a phenyl group.

[0028] In the above general formula (B-1), X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-.

[0029] In the general formula (B-1), R 3 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. R in the above general formula (B-1) 3 The substituent in is R of the general formula (A-1a) 1 The substituents described in the above can be selected as appropriate. The aforementioned R 3 It is more preferable that each of these elements be independently selected from the group consisting of hydrogen, fluorine, and methyl groups.

[0030] The diamine compound represented by the general formula (B-1) has two amino groups (-NH2). When m is 0, the two amino groups can be substituted at any two positions on the benzene ring shown at the left end of the general formula (B-1), and when m is 1, 2, or 3, the two amino groups can be substituted at any two positions on the fused benzene ring.

[0031] [ka]

[0032] In the general formula (B-2), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle, and at least one R 1 It contains a fluorine atom. R in the above general formula (B-2) 1 The substituent in is R of the general formula (A-1a) 1 The substituents described in the above can be selected as appropriate. One of the R 1 is fluorine, and the other R 1 However, each is preferably independently selected from the group consisting of hydrogen, fluorine, and alkyl groups having 1 to 4 carbon atoms; one of the R 1 is fluorine, and the other R 1 However, it is more preferable that each is independently selected from the group consisting of hydrogen, fluorine, and methyl groups.

[0033] In the general formula (B-2) above, each m independently represents an integer between 0 and 2, preferably 0 or 1, and more preferably 0. o represents an integer from 0 to the maximum number of substituents, preferably an integer of 25% or more of the maximum number of substituents, and more preferably an integer of 50% or more of the maximum number of substituents.

[0034] The diamine compound represented by the general formula (B-2) has two amino groups (-NH2). When m is 0, the two amino groups can be substituted at any two positions on the benzene rings shown at both ends of the general formula (B-2), and may be substituted on the same benzene ring or on each of the two benzene rings. When m is 1 or 2, the two amino groups can be substituted at any two positions on the two fused benzene rings, and may be substituted on the same fused benzene ring or on each of the two fused benzene rings.

[0035] In one embodiment, it is preferable that the general formula (B-1) is either the following general formula (B-1a) or the following general formula (B-1b), and it is preferable that the general formula (B-2) is the following general formula (B-2a). The following general formula (B-1a) is one of the embodiments of the above general formula (B-1) where m=0 and n=0. The following general formula (B-1b) is one of the embodiments of the above general formula (B-1) where n=0. The following general formula (B-2a) is one of the embodiments of the above general formula (B-2) where m=0.

[0036] [ka]

[0037] In the general formula (B-1a), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. The aforementioned R 1 Preferably, each of these components is independently selected from the group consisting of fluorine and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of fluorine and a methyl group.

[0038] In the general formula (B-1a) above, o represents an integer from 0 to 4, preferably an integer from 1 to 4, and more preferably an integer from 2 to 4.

[0039] [ka]

[0040] In the general formula (B-1b), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. The aforementioned R 1 Preferably, each of these is independently selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0041] In the general formula (B-1b) above, m represents an integer from 1 to 3, and is preferably 1 or 2, and more preferably 1. o represents an integer from 0 to the maximum number of substituents, preferably an integer of 25% or more of the maximum number of substituents, and more preferably an integer of 50% or more of the maximum number of substituents.

[0042] [ka]

[0043] In the general formula (B-2a), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle, and at least one R 1 It contains a fluorine atom. One of the R 1 is fluorine, and the other R 1 However, each is preferably independently selected from the group consisting of hydrogen, fluorine, and alkyl groups having 1 to 4 carbon atoms; one of the R 1 is fluorine, and the other R 1However, it is more preferable that each is independently selected from the group consisting of hydrogen, fluorine, and methyl groups.

[0044] In the general formula (B-2a) above, o represents an integer from 0 to 8, preferably an integer from 2 to 8, and more preferably an integer from 4 to 8.

[0045] [Second Embodiment] The polyimide resin for low refractive index materials in the second embodiment of this disclosure is a polyimide resin comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more selected from the group consisting of compounds represented by the following general formulas (A-2a) to (A-2g), and the diamine is one or more selected from the group consisting of compounds represented by the following general formula (B-3) and compounds represented by the following general formula (B-4).

[0046] <Acid anhydride> The aforementioned acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formulas (A-2a) to (A-2g). The aforementioned acid anhydride may be used alone or in combination of two or more types.

[0047] [ka]

[0048] In the general formulas (A-2a) to (A-2g), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. From the above general formula (A-2a) to general formula (A-2g), R 1 The substituent in is R of the general formula (A-1a) 1 The substituents described in the above can be selected as appropriate. The aforementioned R 1Preferably, each of these is independently selected from the group consisting of hydrogen, fluorine, C1-C4 alkyl groups, and C1-C4 fluoroalkyl groups, and more preferably selected from the group consisting of hydrogen, fluorine, methyl groups, and trifluoromethyl groups.

[0049] In the general formulas (A-2a) to (A-2g) above, l represents an integer from 1 to 3, and is preferably 1 or 2.

[0050] In the general formulas (A-2a) to (A-2g), R 2 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. From the above general formula (A-2a) to general formula (A-2g), R 2 The substituent in is R of the general formula (A-1a) 1 The substituents described in the above can be selected as appropriate. The aforementioned R 2 Preferably, each of these is independently selected from the group consisting of hydrogen, fluorine, C1-C4 alkyl groups, and C1-C4 fluoroalkyl groups, and more preferably selected from the group consisting of hydrogen, fluorine, methyl groups, and trifluoromethyl groups.

[0051] <Diamine> The aforementioned diamine is one or more compounds selected from the group consisting of compounds represented by the following general formula (B-3) and compounds represented by the following general formula (B-4). In one embodiment, it is preferable that the general formula (B-3) is either the following general formula (B-3a) or the following general formula (B-3b), and it is preferable that the general formula (B-4) is the following general formula (B-4a). The aforementioned diamine may be used alone or in combination of two or more types.

[0052] [ka]

[0053] In the general formula (B-3), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. R in the above general formula (B-3) 1 The substituent in is R of the general formula (A-1a) 1 The substituents described in the above can be selected as appropriate. The aforementioned R 1 Preferably, each of these is independently selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0054] In the general formula (B-3) above, l represents an integer from 1 to 3, preferably 1 or 2, and more preferably 1. m represents an integer between 0 and 3, preferably 0, 1, or 2, and more preferably 0 or 1. n represents an integer between 0 and 5, preferably between 0 and 3, and more preferably 0 or 1. o represents an integer from 0 to the maximum number of substituents, preferably an integer of 25% or more of the maximum number of substituents, and more preferably an integer of 50% or more of the maximum number of substituents.

[0055] In the general formula (B-3), R 2 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and at least one R 2 This is a fluoroalkyl group which may have substituents. R in the above general formula (B-3) 2 The substituent in is R of the general formula (A-1a) 1 The substituents described in the above can be selected as appropriate. One of the R 2 is a fluoroalkyl group having 1 to 4 carbon atoms, and the other R 2 However, each is preferably independently selected from the group consisting of hydrogen, fluorine, alkyl groups having 1 to 4 carbon atoms, and aromatic rings; one of the R 1 is a trifluoromethyl group, and the other R 1 However, it is more preferable that each is independently selected from the group consisting of hydrogen, a methyl group, a trifluoromethyl group, and a phenyl group.

[0056] In the general formula (B-3) above, X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-.

[0057] In the general formula (B-3), R 3 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. R in the above general formula (B-3) 3 The substituent in is R of the general formula (A-1a) 1 The substituents described in the above can be selected as appropriate. The aforementioned R 3 It is more preferable that each of these elements be independently selected from the group consisting of hydrogen, fluorine, and methyl groups.

[0058] [ka]

[0059] In the general formula (B-4), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. R in the above general formula (B-4) 1The substituent in is R of the general formula (A-1a) 1 The substituents described in the above can be selected as appropriate. The aforementioned R 1 Preferably, each of these is independently selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0060] In the general formula (B-4) above, each m independently represents an integer between 0 and 2, preferably 0 or 1, and more preferably 0. o represents an integer from 0 to the maximum number of substituents, preferably an integer of 25% or more of the maximum number of substituents, and more preferably an integer of 50% or more of the maximum number of substituents.

[0061] In one embodiment, it is preferable that the general formula (B-3) is either the following general formula (B-3a) or the following general formula (B-3b), and it is preferable that the general formula (B-4) is the following general formula (B-4a). The following general formula (B-3a) is one of the embodiments of the above general formula (B-3) where m=0 and n=0. The following general formula (B-3b) is one of the embodiments of the above general formula (B-3) where n=0. The following general formula (B-4a) is one of the embodiments of the above general formula (B-4) where m=0.

[0062] [ka]

[0063] In the general formula (B-3a), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. The aforementioned R 1Preferably, each of these components is independently selected from the group consisting of fluorine and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of fluorine and a methyl group.

[0064] In the general formula (B-3a) above, o represents an integer from 0 to 4, preferably an integer from 1 to 4, and more preferably an integer from 2 to 4.

[0065] [ka]

[0066] In the general formula (B-3b), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. The aforementioned R 1 Preferably, each of these is independently selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0067] In the general formula (B-3b) above, m represents an integer from 1 to 3, and is preferably 1 or 2, and more preferably 1. o represents an integer from 0 to the maximum number of substituents, preferably an integer of 25% or more of the maximum number of substituents, and more preferably an integer of 50% or more of the maximum number of substituents.

[0068] [ka]

[0069] In the general formula (B-4a), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle, and at least one R1 It contains a fluorine atom. One of the R 1 is fluorine, and the other R 1 However, each is preferably independently selected from the group consisting of hydrogen, fluorine, and alkyl groups having 1 to 4 carbon atoms; one of the R 1 is fluorine, and the other R 1 However, it is more preferable that each is independently selected from the group consisting of hydrogen, fluorine, and methyl groups.

[0070] In the general formula (B-4a) above, o represents an integer from 0 to 8, preferably an integer from 2 to 8, and more preferably an integer from 4 to 8.

[0071] [Third Embodiment] The polyimide resin for low refractive index materials in the third embodiment of this disclosure is a polyimide resin having the following general formula (1) structural unit, [ka] In the above general formula (1), R a The (CO)4 portion represents a tetravalent group derived from a tetravalent tetracarboxylic acid with 2 or more carbon atoms, R b The (N)2 portion represents a tetravalent group derived from a divalent diamine with two or more carbon atoms. The free volume fraction and average number of neighboring atoms of the amorphous polyimide resin in equilibrium at a temperature of 300K and a pressure of 1atm, as calculated by molecular dynamics calculations, satisfy any of the following conditions (1) to (4): (1) The free volume fraction is 0.23 to 0.32, and the average number of neighboring atoms is 3.90 to 4.60. (2) The free volume fraction is 0.23 to 0.32, the average number of neighboring atoms is 3.90 to 4.60, and it does not contain a trifluoromethyl group. (3) The free volume fraction is 0.24 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not contain a trifluoromethyl group. (4) The free volume fraction is 0.28 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not contain a trifluoromethyl group. The polyimide resin for low refractive index materials is such that the number of adjacent atoms is the total number of atom pairs satisfying both (a) and (b) below. (a) Atomic pairs that share one side of a Voronoi cell, with each atom acting as a parent point. (b) Atomic pairs separated by four or more bonds, or atomic pairs between different molecules

[0072] -Free volume fraction- "Free volume" is the volume per unit mass of a molecule under constant temperature and pressure, i.e., the specific volume v, minus the volume occupied by that molecule v0. This can be expressed as the free volume vf using the following equation 1. Furthermore, the "free volume fraction" is the free volume vf per specific volume v, and can be expressed as the free volume fraction f using the following equation 2. (Formula 1) vf=v-v0 (Formula 2) f=(v-v0) / v

[0073] The free volume fraction in this embodiment is the free volume fraction of the amorphous polyimide resin in equilibrium at a temperature of 300K and a pressure of 1atm, calculated by molecular dynamics calculations, and can be determined by the following formula 3. Specifically, the free volume fraction can be calculated using the polymer property automatic calculation system RadonPy (open-source software) and the Python library molecular dynamics calculation. Based on the coordinates of each atom in the equilibrium state in the molecular dynamics simulation described later, the free volume fraction f can be calculated using the following equation 3. In addition, the van der Waals radii of each atom in Equation 3 below were calculated based on the GAFF2 force field (see Reference 1 below). Reference 1: X. He, VH Man, W. Yang, T.-S. Lee, and J. Wang, A Fast and High-Quality Charge Model for the next Generation General AMBER Force Field, J. Chem. Phys. 153, 114502 (2020).

[0074] (Formula 3)

number

[0075] -Average number of neighboring atoms- The aforementioned average number of neighboring atoms is the average number of neighboring atoms per unit of atoms constituting the molecular dynamics calculation system. The number of adjacent atoms is the total number of atom pairs that satisfy both (a) and (b) below. (a) Atomic pairs that share one side of a Voronoi cell, with each atom acting as a parent point. (b) Atomic pairs separated by four or more bonds, or atomic pairs between different molecules

[0076] Specifically, the number of adjacent atoms is calculated by molecular dynamics simulation as the total number of atom pairs that satisfy both (a) and (b) below. (a) In a Voronoi diagram calculated with each atom as a generator point, pairs of atoms (pairs of generator points) that share a Voronoi edge. (b) Atomic pairs separated by four or more bonds, or atomic pairs between different molecules In a system with periodic boundary conditions, the average number of neighboring atoms can be calculated by dividing the total number of pairs satisfying (a) and (b) above (i.e., the number of neighboring atoms) by the number of atoms constituting the system.

[0077] In this embodiment, the average number of neighboring atoms is the average number of neighboring atoms in the equilibrium state of the amorphous polyimide resin at a temperature of 300K and a pressure of 1atm, calculated by molecular dynamics calculations. Based on the coordinates of each atom in the equilibrium state in the molecular dynamics simulation described later, a Voronoi polyhedron analysis is performed with each atom as a generator point. The average number of neighboring atoms per atom can be calculated by dividing the total number of atom pairs satisfying (a) and (b) in the amorphous cell by the total number of atoms constituting the amorphous cell.

[0078] The free volume fraction and the average number of neighboring atoms satisfy any of the following conditions (1) to (4). As shown in the molecular dynamics simulation described later, it is possible to achieve both a low refractive index of 1.57 or less and a low coefficient of thermal expansion of 50 ppm / K or less when either of the following conditions (1) or (2) is met.

[0079] (1) The free volume fraction is 0.23 to 0.32, and the average number of neighboring atoms is 3.90 to 4.60. When the above condition (1) is met, it is possible to achieve both a low refractive index of 1.57 or less and a low coefficient of thermal expansion of 40 ppm / K or less.

[0080] (2) The free volume fraction is 0.23 to 0.32, the average number of neighboring atoms is 3.90 to 4.60, and it does not have a trifluoromethyl group. When the above condition (2) is met, it is possible to achieve both a low refractive index of 1.57 or less and a low coefficient of thermal expansion of 40 ppm / K or less.

[0081] (3) The free volume fraction is 0.24 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not have a trifluoromethyl group. When the above condition (3) is met, it is possible to achieve both a low refractive index of 1.57 or less and a low coefficient of thermal expansion of 30 ppm / K or less.

[0082] (4) The free volume fraction is 0.28 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not have a trifluoromethyl group. When the above condition (4) is met, it is possible to achieve both a low refractive index of 1.57 or less and a low coefficient of thermal expansion of 20 ppm / K or less.

[0083] [Fourth Embodiment] The polyimide resin for low refractive index materials in the fourth embodiment of this disclosure is the polyimide resin for low refractive index materials in the first embodiment, or the polyimide resin for low refractive index materials in the second embodiment, The free volume fraction and average number of neighboring atoms of the amorphous polyimide resin in equilibrium at a temperature of 300K and a pressure of 1atm, as calculated by molecular dynamics calculations, satisfy any of the following conditions (1) to (4): (1) The free volume fraction is 0.23 to 0.32, and the average number of neighboring atoms is 3.90 to 4.60. (2) The free volume fraction is 0.23 to 0.32, the average number of neighboring atoms is 3.90 to 4.60, and it does not contain a trifluoromethyl group. (3) The free volume fraction is 0.24 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not contain a trifluoromethyl group. (4) The free volume fraction is 0.28 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not contain a trifluoromethyl group. The average number of neighboring atoms is the average number of neighboring atoms per number of atoms constituting the molecular dynamics calculation system, The polyimide resin for low refractive index materials is such that the number of adjacent atoms is the total number of atom pairs satisfying both (a) and (b) below. (a) Atomic pairs that share one side of a Voronoi cell, with each atom acting as a parent point. (b) Atomic pairs separated by four or more bonds, or atomic pairs between different molecules

[0084] The polyimide resin for the low refractive index material in the first embodiment and the polyimide resin for the low refractive index material in the second embodiment can be appropriately selected from the items described in the first embodiment and the second embodiment, respectively. The conditions for the free volume fraction and the average number of neighboring atoms can be appropriately selected from those described in the third embodiment. The free volume fraction and the average number of neighboring atoms are preferably such that they satisfy condition (1) or (2) and any of conditions (3) to (6).

[0085] [Characteristics] Each of the polyimide resins for low refractive index materials in the first to fourth embodiments preferably has a refractive index of 1.57 or less and a coefficient of linear expansion of 50 ppm / K or less.

[0086] -Refractive index- The refractive index of the polyimide resin is preferably 1.57 or less.

[0087] Specifically, the refractive index of the polyimide resin can be measured using a refractive index measuring device (for example, an Abbe refractometer NAR-1T SOLID, manufactured by Atago Co., Ltd.) at 25°C and a wavelength of 589 nm for a polyimide film obtained by the polyimide film manufacturing method described later.

[0088] Furthermore, a specific method for determining the refractive index of the polyimide resin by molecular dynamics simulation is the following procedure, as will be explained in the molecular dynamics simulation described later. Based on the following equation, quantum chemical calculations determine the polarizability α of the monomer unit. unit , and the polarizability α of the terminal group edgeAfter obtaining [the relevant value], the polarization rate α of the entire system is calculated from the information on the degree of polymerization m and the number of molecules N. For the calculation of the polarization rates of the monomer units and end groups, Gaussian16 is used for quantum chemical calculations, and calculations are performed at the ωB97XD / 6-31G(d,p) level for structural optimization calculations and at the ωB97XD / 6-311++G(2d,p) level for polarization rate calculations.

[0089]

Number

[0090] Next, the refractive index n was calculated using the Lorentz-Lorenz equation (the following equation). For the volume V of the system, the value obtained by the molecular dynamics simulation described later is used.

[0091]

Number

[0092] -Coefficient of linear expansion- The coefficient of linear expansion means the ratio of the amount of deformation ΔL per 1 K (Kelvin) or 1 °C temperature change to the original length L. As the coefficient of linear expansion of the polyimide resin, 50 ppm / K or less is preferable, 40 ppm / K or less is more preferable, 30 ppm / K or less is still more preferable, and 20 ppm / K or less is particularly preferable.

[0093] Specifically, the coefficient of linear expansion of the polyimide resin can be measured for the polyimide film obtained by the method for producing a polyimide film described later, using a thermomechanical analyzer (EXSTAR6000TMA / SS6000, manufactured by SII NanoTechnology Inc.) under the following measurement conditions. --Measurement conditions-- First stage: Heat up to 150 °C at a heating rate of 5 °C per minute to remove the adsorbed water of the sample. Second stage: Air-cool to room temperature at a cooling rate of 5 °C per minute. Third stage: Perform this measurement at a heating rate of 5 °C per minute. Obtain the average value of the coefficient of linear expansion within the temperature range of 50°C to 200°C for this measurement, and use it as the coefficient of linear expansion of the target polyimide film.

[0094] Also, as a method for obtaining the calculated value of the coefficient of linear expansion of the polyimide resin by molecular dynamics simulation, specifically, the following procedure can be mentioned as described in the molecular dynamics simulation to be described later. First, based on the fluctuations of volume V and enthalpy H in the equilibration calculation, calculate the volume expansion rate α from the following formula [see Reference 2 below]. k P represents the Boltzmann constant, and T represents the temperature. B is the Boltzmann constant, and T is the temperature. Reference 2: M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon Press, New York, 1989).

[0095]

Equation

[0096] Next, assuming the isotropy of the system, derive the coefficient of linear expansion α from the following formula. L is derived.

[0097]

Equation

[0098] -Glass transition point- As the glass transition temperature of the polyimide resin, 260°C or higher is preferable, 280°C or higher is more preferable, and 300°C or higher is even more preferable. When the glass transition temperature is 260°C or higher, a low refractive index material with good solder heat resistance and dimensional stability can be obtained.

[0099] -Haze- The haze of the polyimide resin is preferably 20% or less, more preferably 10% or less, and even more preferably 5% or less. When the haze is 20% or less, transparency can be obtained when used as a cladding material or optical waveguide, making it suitable for use.

[0100] The haze of the polyimide resin can be measured specifically using a spectroscopic haze meter (HSP-150Vis, manufactured by Murakami Color Technology Laboratory Co., Ltd.) on a polyimide film obtained by the polyimide film manufacturing method described later. The average thickness of the polyimide film used as the measurement sample is preferably 5 μm to 80 μm.

[0101] -Transmittance- The transmittance of the polyimide resin is preferably 80% or higher, and more preferably 90% or higher, as measured using a spectrophotometer at a wavelength of 550 nm with a polyimide film having an average thickness of 100 μm. The upper limit of the transmittance is not limited, but for example, it may be 98%.

[0102] -Elongation at break- The elongation at break of the polyimide resin is preferably 20% or more, more preferably 25% or more, and even more preferably 30% or more. When the break elongation is 20% or more, tearing during film transport is less likely to occur in the polyimide film manufacturing process, thus maintaining good productivity. Furthermore, bending resistance is maintained when it is made into a flexible printed circuit board, making cracking and wiring breakage less likely during the mounting process.

[0103] -Tensile modulus- The tensile modulus of the polyimide resin is preferably 5 GPa or higher, more preferably 6 GPa or higher, and even more preferably 7 GPa or higher. When the tensile modulus is 5 GPa or higher, the amount of elongation of the film when tension is applied during film transport in the polyimide film manufacturing process is suppressed, and dimensional stability is maintained.

[0104] Specifically, the elongation at break and tensile modulus of the polyimide resin can be measured using a Tensilon universal material tester (RTM-100, manufactured by Orientec Co., Ltd.) in accordance with Japanese Industrial Standards (JIS K 7127:1999), with a sample cut into strips 10 mm wide and 80 mm long from a polyimide film obtained by the polyimide film manufacturing method described later. The width of the sample to be measured is 10 mm, the chuck spacing is 50 mm, the test speed is 50 mm / minute, and the average value is calculated with n=10 measurements.

[0105] [Method for synthesizing polyimide resin] There are no particular limitations on the method for synthesizing the polyimide resin, and a known method can be appropriately selected depending on the purpose. For example, polyamic acid (polyamic acid), which is a precursor of polyimide, can be synthesized by polymerizing equimolar amounts of acid anhydride and diamine, and the obtained polyamic acid can be heated at a temperature of 200°C or higher, or an imidation (dehydration and cyclization) reaction can be carried out using a catalyst to obtain polyimide. Alternatively, a tetracarboxylic acid corresponding to the acid anhydride may be used in place of, or in combination with, the acid anhydride. When multiple acid anhydrides and / or multiple diamines are used, the resulting polyamic acid and polyimide resin may be random copolymers, block copolymers, or mixtures thereof.

[0106] The polyamic acid and the composition containing the polyamic acid can be synthesized, for example, by the following procedure. A thermometer and a stirring rod with stirring blades are set in a 300 mL four-neck separable flask. Next, a solvent (e.g., dimethylacetamide, DMAC) is added under a stream of dry nitrogen and the temperature is raised to 60°C. After the temperature rises, the diamine is added while stirring and dissolved. Then, equimolar amounts of acid anhydride are added and stirred to polymerize the acid anhydride and diamine. After that, the mixture is cooled to room temperature, and if necessary, solvent is added and the mixture is filtered to obtain a composition containing polyamic acid.

[0107] As the reaction temperature for polymerizing the acid anhydride and the diamine, -20°C to 150°C is preferable, and 0 to 100°C is more preferable. As the reaction time, 0.1 hour to 24 hours is preferable, and 0.5 hour to 12 hours is more preferable. Also, it is preferable that the number of moles of the acid anhydride used in the reaction is equal to the number of moles of the diamine. A polyamic acid in which the acid anhydride and the diamine are closer to an equal amount is more likely to yield a polyimide film with high mechanical properties.

[0108] As a method for synthesizing the polyimide from the polyamic acid by an imidization reaction, for example, the following procedure can be cited. Apply (for example, spin coat) the composition containing the obtained polyamic acid onto a substrate. Then, dry it using a hot plate (for example, at 80°C for 5 minutes). Subsequently, a film-like polyimide resin can be formed on the substrate by heating at a temperature of 200°C or higher. As a method for heating at the temperature of 200°C or higher, for example, using an oven, in a nitrogen atmosphere (oxygen concentration 20 ppm or less), raise the temperature from 50°C at a rate of 4°C per minute, heat at 180°C for 30 minutes, and then continue heating at 350°C for 30 minutes, etc. can be cited.

[0109] [Method for Identifying Polyimide Resin] The method for identifying the polyimide resin is not particularly limited and can be appropriately selected according to the purpose. For example, a method of analyzing by the infrared attenuated total reflection method (IR-ATR method) using a Fourier transform infrared spectrometer (FT-IR) to identify constituent components such as acid anhydrides and diamines can be cited. The measurement of FT-IR can be performed, for example, using Nicolet 6700 (manufactured by Thermo Fisher Scientific Co., Ltd.).

[0110] (Polyamic Acid for Low Refractive Index Material) The polyamic acid for low refractive index materials of this disclosure is a precursor of the polyimide resin for low refractive index materials of this disclosure, which is used in applications of low refractive index materials and achieves both a low refractive index and a low coefficient of thermal expansion, and is a polyamic acid that is (1) a precursor of the polyimide resin for low refractive index materials in the first embodiment, or (2) a precursor of the polyimide resin for low refractive index materials in the second embodiment.

[0111] [First Embodiment] The polyamic acid for low refractive index materials in the first embodiment of this disclosure is a precursor of the polyimide resin for low refractive index materials in the first embodiment, and is a polyamic acid comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more selected from the group consisting of the compound represented by the general formula (A-1a) and the compound represented by the general formula (A-1b), and the diamine is one or more selected from the group consisting of the compound represented by the general formula (B-1) and the compound represented by the general formula (B-2).

[0112] The acid anhydride and the diamine can be appropriately selected from those described in the description of the polyimide resin for low refractive index materials in the first embodiment.

[0113] [Second Embodiment] The polyamic acid for low refractive index materials in the second embodiment of this disclosure is a precursor of the polyimide resin for low refractive index materials in the second embodiment, and comprises an acid anhydride and a diamine, wherein the acid anhydride is one or more selected from the group consisting of compounds represented by the following general formulas (A-2a) to (A-2g), and the diamine is one or more selected from the group consisting of compounds represented by the following general formula (B-3) and compounds represented by the following general formula (B-4).

[0114] The acid anhydride and the diamine can be appropriately selected from those described in the polyimide resin for low refractive index materials in the second embodiment.

[0115] (Composition for low refractive index materials) [First Embodiment] The composition for low refractive index materials in the first embodiment of this disclosure contains a polyimide resin and may further contain other components such as a solvent as needed. Suitable examples of the polyimide resin include the polyimide resin for low refractive index materials in the first embodiment, the polyimide resin for low refractive index materials in the second embodiment, the polyimide resin for low refractive index materials in the third embodiment, and the polyimide resin for low refractive index materials in the fourth embodiment. These may be used individually or in combination of two or more types. The composition for low refractive index materials in the first embodiment can be suitably prepared by imidizing the composition for low refractive index materials in the second embodiment.

[0116] [Second Embodiment] The composition for low refractive index materials in the second embodiment of the present disclosure comprises a polyamic acid and a solvent, and may further contain other components as needed. Suitable examples of the polyamic acid include the polyamic acid for low refractive index materials in the first embodiment and the polyamic acid for low refractive index materials in the second embodiment. These may be used individually or in combination of two or more.

[0117] <Solvent> The aforementioned solvent is not particularly limited and can be appropriately selected depending on the purpose. Examples include water, N-methyl-2-pyrrolidone, N,N-dimethylformamide, N,N-dimethylacetamide, N,N-dimethylisobutylamide, 3-methoxy-N,N-dimethylpropionamide, 3-butoxy-N,N-dimethylpropionamide, γ-butyrolactone, ethyl lactate, 1,3-dimethyl-2-imidazolidinone, N,N'-dimethylpropyleneurea, 1,1,3,3-tetramethylurea, dimethyl sulfoxide, sulfolane, propylene glycol monomethyl ether, propylene glycol monomethyl ether acetate, diethylene glycol ethyl methyl ether, and diethylene glycol dimethyl ether. These may be used individually or in combination of two or more types.

[0118] There are no particular restrictions on the content of the solvent, and it can be appropriately selected depending on the purpose, but it is preferably 150 parts by mass or more, and more preferably 200 parts by mass or more, per 100 parts by mass of polyimide resin and / or polyamic acid in the composition. Furthermore, the solvent content is preferably 2000 parts by mass or less, and more preferably 1000 parts by mass or less. When the solvent content is between 150 parts by mass and 2000 parts by mass, the viscosity becomes suitable for coating, and the thickness of the coated composition and the resulting polyimide film can be easily adjusted.

[0119] <Other ingredients> Examples of the other components mentioned above include catalysts that catalyze imidation and dehydrating agents.

[0120] -catalyst- Examples of the catalysts mentioned above include amines. Examples of the aforementioned amines include aliphatic tertiary amines such as trimethylamine and triethylenediamine; aromatic tertiary amines such as dimethylaniline; and heterocyclic tertiary amines such as isoquinoline, pyridine, and β-picoline. These may be used individually or in combination of two or more. Among these, heterocyclic tertiary amines are preferred, and β-picoline is more preferred.

[0121] -Dehydrating agent- Examples of the dehydrating agent include aliphatic carboxylic acid anhydrides such as acetic anhydride, propionic anhydride, and butyric anhydride; and aromatic carboxylic acid anhydrides such as benzoic anhydride. These may be used individually or in combination of two or more. Among these, acetic anhydride and benzoic anhydride are preferred, with acetic anhydride being more preferred.

[0122] The respective contents of the catalyst and dehydrating agent are not particularly limited and can be appropriately selected depending on the purpose, but are preferably 0.05 to 10 moles, more preferably 0.1 to 5 moles, and even more preferably 0.5 to 3 moles per mole of amic acid units of polyamic acid.

[0123] Furthermore, the composition for the low refractive index material in the first embodiment may also contain other components such as inorganic particles, thermal crosslinking agents, thermal acid generators, leveling agents, viscosity modifiers, antioxidants, inorganic pigments, organic pigments, and dyes.

[0124] -Inorganic particles- The composition for low refractive index materials in the first embodiment, and the polyimide film described later, may contain inorganic particles for the purpose of further improving the heat resistance of the polyimide film or reducing its coefficient of thermal expansion. Examples of the inorganic particles include metal inorganic particles such as platinum, gold, palladium, silver, copper, nickel, zinc, aluminum, iron, cobalt, rhodium, ruthenium, tin, lead, bismuth, and tungsten; and metal oxide inorganic particles such as silicon dioxide (silica), titanium dioxide, aluminum oxide, zinc oxide, tin oxide, tungsten oxide, zirconium oxide, calcium carbonate, and barium sulfate. There are no particular restrictions on the shape or content of the inorganic particles, and they can be appropriately selected depending on the purpose. Furthermore, it is preferable to uniformly disperse the inorganic particles in the composition and the polyimide film, and known methods can be applied.

[0125] (Polyimide film for low refractive index materials) The polyimide film for low refractive index materials of this disclosure contains a polyimide resin and may further contain other components as needed. Suitable examples of the polyimide resin include the polyimide resin for low refractive index materials in the first embodiment, the polyimide resin for low refractive index materials in the second embodiment, the polyimide resin for low refractive index materials in the third embodiment, and the polyimide resin for low refractive index materials in the fourth embodiment. These may be used individually or in combination of two or more types.

[0126] The average thickness of the polyimide film is not particularly limited and can be appropriately selected depending on the purpose, but it is preferably 3 μm or more, more preferably 5 μm or more, and even more preferably 10 μm or more. If the average thickness is 3 μm or more, sufficient mechanical properties can be obtained for use as a circuit board. Furthermore, the average thickness is preferably 200 μm or less, more preferably 100 μm or less, and even more preferably 80 μm or less. If the average thickness is 80 μm or less, sufficient toughness can be obtained for use as a circuit board.

[0127] The polyimide film can be suitably used in optical components such as lenses, filters, optical fibers, mirrors, refractive optical elements, and diffractive optical elements; as well as in light-emitting device components, light-absorbing device components, and display device components.

[0128] [Method for manufacturing polyimide film] There are no particular limitations on the method for producing the polyimide film, and an appropriate method can be selected depending on the purpose. For example, (I) a method comprising the steps of coating and drying a composition containing polyamic acid on a substrate, and heating the resulting coating to imide it; (II) a method comprising the steps of casting a composition containing polyamic acid on a heated substrate to imide it and form a gel film, peeling the gel film obtained from the substrate, and heat-treating the peeled gel film.

[0129] There are no particular restrictions on the substrate, and it can be appropriately selected according to the purpose. Examples include glass substrates; metal substrates such as stainless steel drums, endless stainless steel belts, and aluminum foil. The temperature of the substrate is preferably 30°C to 200°C, more preferably 40°C to 150°C, and even more preferably 50°C to 120°C. The drying temperature of the gel film is preferably 150°C to 500°C, more preferably 180°C to 400°C, and even more preferably 200°C to 300°C. The heat treatment temperature for the polyimide film after drying is preferably 200°C or higher, more preferably 300°C or higher, and even more preferably 350°C or higher. The gel film and polyimide film may be stretched in the transport direction or the width direction during each step.

[0130] The resulting polyimide film may be further subjected to annealing or adhesion-enhancing treatments (e.g., electrolytic treatments such as corona treatment or plasma treatment, or blast treatment).

[0131] (optical materials) Applications of the optical materials disclosed herein include cladding materials for optical fibers, cladding materials for optical waveguides, pellicle materials, surface protection materials for displays (e.g., PDP, LCD, FED, organic EL, etc.), surface protection materials for lenses (e.g., focusing lenses for light-emitting elements, artificial crystalline lenses, contact lenses, low refractive index lenses, etc.), materials for lenses (e.g., focusing lenses for light-emitting elements, artificial crystalline lenses, contact lenses, low refractive index lenses, etc.), and sealing materials for devices (e.g., light-emitting elements, solar cell elements, semiconductor elements, etc.). Other applications include use in various optical sealing materials and optical encapsulants that require chemical resistance, weather resistance, heat resistance, moisture resistance, and oil resistance.

[0132] (Clad material) The clad material of this disclosure contains a polyimide resin and may further contain other components as needed.

[0133] (optical waveguide) The optical waveguide of the present disclosure has the cladding material of the present disclosure and may further have other components such as a substrate and a core material, as necessary.

[0134] Figures 1 and 2 show cross-sectional views of an optical waveguide. The optical waveguide 1 comprises a core material 4 made of a resin composition for forming a core with a relatively high refractive index, and a cladding material 3 with a relatively low refractive index, and further comprises an optical waveguide substrate 2, on which the optical waveguide 1 may be formed. The core material 4 is arranged to be embedded in the cladding material 3. As shown in Figure 2, the cladding material 3 may have a lower cladding layer 3a arranged below the core material 4 and an upper cladding layer 3b arranged above the core material 4. The polyimide resin and polyimide film of this disclosure are preferably used in at least one of the cladding material 3 and core material 4, and are more preferably used in the cladding material 3 from the viewpoint of low refractive index, insulation properties, and high heat resistance reliability.

[0135] There are no particular restrictions on the substrate 2 for the optical waveguide, and it can be appropriately selected according to the purpose. Examples include resin, glass, metal, and combinations thereof. Examples of the aforementioned resins include polyesters such as polyethylene terephthalate, polybutylene terephthalate, and polyethylene naphthalate; polyolefins such as polyethylene, polypropylene, and polystyrene; and polycarbonates, polyamides, polyimides, polyamide-imides, polyetherimides, polyether sulfides, polyethersulfones, polyetherketones, polyphenylene ethers, polyphenylene sulfides, polyarylates, polysulfones, and liquid crystal polymers. Among the aforementioned substrates, it is preferable to use a hard substrate such as a silicon substrate, a glass substrate, or a glass epoxy resin substrate such as FR-4. Alternatively, a flexible and tough substrate film may be used as the substrate 2 for the optical waveguide to create a flexible optical waveguide.

[0136] There are no particular restrictions on the average thickness of the lower cladding layer 3a, but 2 μm to 200 μm is preferred. If it is 2 μm or more, the propagation light is prevented from being absorbed or scattered by the optical waveguide substrate 2, and if it is 200 μm or less, the overall thickness of the optical waveguide 1 is prevented from becoming too thick. The thickness of the lower cladding layer 3a is the value from the boundary between the core portion 4 and the lower cladding layer 3a to the bottom surface of the lower cladding layer 3a.

[0137] There are no particular restrictions on the average height of the core material 4, but it is preferably 10 μm to 100 μm, more preferably 15 μm to 80 μm, and even more preferably 20 μm to 70 μm. If the height of the core is 10 μm or more, the alignment tolerance can be increased when coupling with the light-emitting / receiving device or optical fiber after optical waveguide formation. If it is 100 μm or less, the coupling efficiency can be increased when coupling with the light-emitting / receiving device or optical fiber after optical waveguide formation.

[0138] The average thickness of the upper cladding layer 3b is not particularly limited as long as it can cover the core material 4, but a thickness of 12 μm to 500 μm after drying is preferred. The thickness of the upper cladding layer 3b may be the same as or different from the thickness of the lower cladding layer 3a, but from the viewpoint of embedding the core material 4, it is preferable to make it thicker than the lower cladding layer 3a. The thickness of the upper cladding layer 3b is the value from the boundary between the core material 4 and the lower cladding layer 3a to the top surface of the upper cladding layer 3b.

[0139] [Manufacturing method for optical waveguides] There are no particular limitations on the method for manufacturing the optical waveguide, and it can be appropriately selected depending on the purpose. Examples include a method using a resin composition for forming a core material and a resin composition for forming a cladding material by a spin coating method, or a method using a resin film for forming a core material and a resin film for forming a cladding material by a lamination method. These methods can also be combined. Among these, the method using a resin film for forming an optical waveguide and a lamination method is preferred from the viewpoint of providing an optical waveguide manufacturing process with excellent productivity. [Examples]

[0140] The present invention will be described more specifically below based on examples, but the present invention is not limited to the following examples.

[0141] <Molecular dynamics simulation of polyimides> Molecular dynamics simulations were performed on homopolymers with specific structural units to calculate the free volume fraction of the amorphous state and the average number of neighboring atoms. Specifically, following steps S1 to S3 below, we used appropriate computing equipment (including input devices, output devices, CPU, memory, etc.) and the polymer property automatic calculation system RadonPy (open-source software) to obtain the structure in equilibrium state, and calculated the free volume fraction from the equilibrium structure. In addition, we used a proprietary Python program to calculate the average number of neighboring atoms from the equilibrium structure using a Voronoi diagram method.

[0142] Specifically, the polyimides used in the calculations included approximately 250 different types, such as those described in PolyInfo (https: / / polymer.nims.go.jp / ) and PI1M (Reference 3: Ruimin Ma and Tengfei Luo, J. Chem. Inf. Model., 60, 10 (2020)), and molecular dynamics simulations were performed for each polyimide.

[0143] Step S1 Data on the amorphous structure of polyimide, a homopolymer with specific structural units, was obtained. A system was constructed consisting of 10 polyimide molecules, each containing approximately 1000 atoms (more specifically, between 900 and 1100 atoms). The system, in an aggregated state, was cooled from 800K to 300K under a pressure of 1 atm. The cooling rate was 150 ps / K. This allowed for the acquisition of data on the initial structure of the amorphous system. Furthermore, the force field developed in Reference 4 below was used in this calculation, and the non-bonding and bonding interaction parameters were defined. Reference 4: J. Trag and D. Zahn, Improved GAFF2 Parameters for Fluorinated Alkanes and Mixed Hydro- and Fluorocarbons, J. Mol. Model. 25, 39 (2019).

[0144] Step S2 Next, molecular dynamics simulations were used to calculate the motion of each atom under conditions of a temperature of 300 K and a pressure of 1 atm. The coordinates of each atom in the system at equilibrium after 500 ns were obtained.

[0145] <Calculation of free volume fraction using molecular dynamics simulation> Step S3-1 Next, the free volume fraction f was calculated using the polymer property automatic calculation system RadonPy based on the coordinates of each atom at the final time point. The free volume fraction was derived using Equation 3 below, and the van der Waals radii of each atom in Equation 3 below were calculated based on the GAFF2 force field (reference 1 above).

[0146] (Formula 3)

number

[0147] <Calculation of the average number of neighboring atoms using molecular dynamics simulation> Step S3-2 Next, based on the coordinates of each atom at the final time point, the average number of neighboring atoms in the system was calculated using the following method. The number of adjacent atoms was calculated as the total number of atom pairs that satisfy both (a) and (b) below. (a) In a Voronoi diagram calculated with each atom as a generator point, pairs of atoms (pairs of generator points) that share a Voronoi edge. (b) Atomic pairs separated by four or more bonds, or atomic pairs between different molecules Next, the average number of neighboring atoms was calculated by dividing the total number of pairs (i.e., the number of neighboring atoms) that satisfy both (a) and (b) above within a system with periodic boundary conditions by the number of atoms constituting the system.

[0148] <Calculation of refractive index using molecular dynamics simulation> The refractive index was calculated using the following procedure. Based on the following equation, quantum chemical calculations determine the polarizability α of the monomer unit. unit , and the polarizability α of the terminal group edge After determining the degree of polymerization m and the number of molecules N, the polarizability α of the entire system was calculated. For the calculation of the polarizability of monomer units and terminal groups, Gaussian16 was used for quantum chemical calculations, and calculations at the level of ωB97XD / 6-31G(d,p) were performed for structural optimization calculations, and ωB97XD / 6-311++G(2d,p) were performed for polarizability calculations.

[0149]

number

[0150] Next, the refractive index n was calculated using the Lorentz-Lorentz equation (shown below). The volume V of the system was obtained from the molecular dynamics simulation described later.

[0151]

number

[0152] <Calculation of linear expansion coefficient using molecular dynamics simulation> First, based on the fluctuations of volume V and enthalpy H in the equilibrium calculation, the volume expansion coefficient α is obtained from the following equation. P k was calculated. B is the Boltzmann constant, and T represents temperature.

[0153]

number

[0154] Next, assuming the isotropy of the system, the coefficient of linear expansion α is given by the following equation. L This was derived.

[0155]

number

[0156] Figure 3 is a graph plotting the free volume fraction against the average number of neighboring atoms. In Figure 3, dots that satisfy the coefficient of linear expansion and refractive index of 60 ppm / K or less and 1.52 or less, respectively, as calculated by molecular dynamics simulation, are shown in black.

[0157] Figure 4 is a graph plotting the measured refractive index and linear thermal expansion coefficient for various polymers. The measured values ​​were referenced from those listed on PolyInfo. Figure 4 suggests that there is generally a negative correlation between the two properties (correlation coefficient: -0.74), indicating that it is difficult to achieve both a low coefficient of thermal expansion and a low refractive index simultaneously.

[0158] Therefore, when we visualized polyimides (black dots) that exhibit both low thermal expansion coefficient and low refractive index in Figure 3, we found that polyimides with low refractive index and low thermal expansion coefficient exist in regions with high free volume fraction and low average number of neighboring atoms. Specifically, it was found that a low refractive index and a low coefficient of thermal expansion can be achieved simultaneously when any of the following conditions (1) to (4) are met regarding the free volume fraction and the average number of neighboring atoms. (1) The free volume fraction is 0.23 to 0.32, and the average number of neighboring atoms is 3.90 to 4.60. (2) The free volume fraction is 0.23 to 0.32, the average number of neighboring atoms is 3.90 to 4.60, and it does not contain a trifluoromethyl group. (3) The free volume fraction is 0.24 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not contain a trifluoromethyl group. (4) The free volume fraction is 0.28 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not contain a trifluoromethyl group.

[0159] The reason why polyimides with a high free volume fraction of 0.23 or higher exhibit the characteristics of a low refractive index and a low coefficient of thermal expansion is as follows. Polyimides with a high free volume fraction (FRF) are characterized by a rigid or bulky molecular structure. In the amorphous state, polyimides with a rigid molecular structure maintain a rod-like shape in their molecular chains regardless of the surrounding molecular arrangement. This makes it difficult for the molecular chains to flexibly change structure and pack densely, resulting in a sparse structure. Similarly, polyimides with a bulky molecular structure are thought to have a sparse structure because the bulky parts act as steric hindrance, inhibiting the free internal rotation of the molecular chains. This suppresses flexible structural changes and dense packing, resulting in a sparse structure. A sparse structure results in relatively smaller polarization per unit volume compared to a dense structure, thus contributing to a reduction in refractive index. Therefore, polyimides with a high free volume fraction, characterized by a rigid or bulky molecular structure, are considered to have a low refractive index. Furthermore, in polyimides with a rigid or bulky structure, it is assumed that internal rotation of the molecular chains is inhibited for the reasons mentioned above, and therefore the change in molecular mobility due to thermal energy (change in conformational rotation frequency) is considered to be small. A small change in molecular mobility due to thermal energy means that the change in free volume with respect to temperature changes is small, which in turn means that the coefficient of thermal expansion is small and the material has a low coefficient of linear expansion. Therefore, polyimides with a rigid or bulky molecular structure and a high free volume fraction are considered to have a low coefficient of linear expansion. For the reasons stated above, a high free volume fraction with a value of 0.23 or higher contributes to a low refractive index and a low coefficient of thermal expansion.

[0160] Polyimides with a low average number of neighboring atoms (4.60 or less) are polyimides with a high content of sp3 hybridized carbon atoms, such as polyimides containing aliphatic or alicyclic structures. Because sp3 hybridized carbon atoms are surrounded by bonding atoms, the probability of them coming into contact with unbonded atoms is low. The average number of neighboring atoms represents the average number of unbonded atoms surrounding each atom; therefore, the higher the content of sp3 hybridized carbon atoms, the lower the average number of neighboring atoms. In contrast, aromatic polyimides containing many sp2 hybridized carbon atoms tend to exhibit a relatively high refractive dielectric constant because the contribution of π electrons, which have high polarizability, is included in the refractive index. Therefore, as the ratio of sp3 hybridized carbon atoms to sp2 hybridized carbon atoms increases, the contribution of π electrons becomes relatively smaller, and the refractive index decreases. Consequently, a low average number of neighboring atoms, such as 4.95 or less, contributes to a low refractive index.

[0161] From the above, it was found that a high free volume fraction contributes to a low refractive index and a low coefficient of thermal expansion, and a low average number of neighboring atoms contributes to a low refractive index. Therefore, it was found that polyimides that satisfy any of the above conditions (1) to (4) have a high free volume fraction and a low average number of neighboring atoms can achieve both a low refractive index and a low coefficient of thermal expansion.

[0162] <Comparison between experimental values ​​and calculated values ​​from molecular dynamics simulations> Regarding the properties of polyimides, specifically refractive index and coefficient of thermal expansion, we compared the experimental values ​​for each polyimide for which experimental values ​​are publicly known with the calculated values ​​obtained from molecular dynamics simulations. The results are shown in Figures 5-6. Specifically, the polyimides for which experimental values ​​are publicly known were those listed in PolyInfo.

[0163] Figure 5 is a graph showing the relationship between experimental values ​​and calculated values ​​from molecular dynamics simulations for the refractive index, and Figure 6 is a graph showing the relationship between experimental values ​​and calculated values ​​from molecular dynamics simulations for the coefficient of linear expansion. In Figures 5 and 6, each dot represents a polyimide for which experimental values ​​are publicly known among several polyimides for which molecular dynamics simulations were performed. The horizontal axis represents experimental values, and the vertical axis represents calculated values. The correlation coefficients were 0.88 (Figure 5) and 0.91 (Figure 6), respectively, indicating a positive correlation in both cases.

[0164] Figures 5-6 show that the refractive index and coefficient of thermal expansion obtained through molecular dynamics simulations qualitatively represent the experimental values. From the above, it was found that the two parameters that can achieve both a low refractive index and a low coefficient of thermal expansion (calculated value): the free volume fraction and the average number of neighboring atoms, as indicated by the aforementioned conditions (1) or (2), also correlate with the experimental values ​​of the refractive index and the coefficient of thermal expansion.

[0165] (Synthesis Example 1) 3.5 g of 2,3,5,6-tetramethyl-1,4-phenylenediamine (TMPD), 4.8 g of 1,2,4,5-cyclohexanetetracarboxylic dianhydride (HPMDA), and N-methyl-2-pyrrolidone (NMP) were added to a flask and stirred at 25°C for 96 hours to synthesize polyamic acid. The obtained polyamic acid A had an Mw of 0.7 million. [ka]

[0166] Although embodiments have been described above, it should be understood that various modifications to the form and details are possible without departing from the spirit and scope of the claims. [Explanation of symbols]

[0167] 1 Optical waveguide 2 Base material for optical waveguide 3 clad 4 cores 10,20 Optical waveguide

Claims

1. It consists of an acid anhydride and a diamine, The acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formula (A-1a) and compounds represented by the following general formula (A-1b). A polyimide resin for low refractive index materials, wherein the diamine is one or more selected from the group consisting of compounds represented by the following general formula (B-1) and compounds represented by the following general formula (B-2). 【Chemistry 1】 In the above general formula (A-1a), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R １ It has a fluorine atom, m represents an integer between 0 and 3. 【Chemistry 2】 In the general formula (A-1b), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. n represents an integer from 1 to 5. R ２ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ２ These may bond to each other to form a cycloalkyl group. at least one R ２ This is a fluoroalkyl group which may have substituents, X is, independently of each other, selected from the group consisting of -O-, -C(R ３ ), ２ -, and -SO ２ - R ３ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ３ These may bond to each other to form a cycloalkyl group. 【Transformation 3】 In the general formula (B-1), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. m represents an integer between 0 and 3. n represents an integer from 0 to 5. o represents an integer from 0 to the maximum number of substituents. R ２ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ２ These may bond to each other to form a cycloalkyl group. at least one R ２ This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R ３ ) ２ -, and -SO ２ - Selected from the group consisting of, R ３ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ３ These may bond to each other to form a cycloalkyl group. 【Chemistry 4】 In the general formula (B-2), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R １ It has a fluorine atom, Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and the maximum number of substituents.

2. The above general formula (B-1) is either the following general formula (B-1a) or the following general formula (B-1b), The polyimide resin according to claim 1, wherein the general formula (B-2) is the following general formula (B-2a). 【Transformation 5】 In the general formula (B-1a), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. 'o' represents an integer between 0 and 4. 【Transformation 6】 In the general formula (B-1b), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. m represents an integer between 1 and 3. 'o' represents an integer between 0 and the maximum number of substituents. 【Transformation 7】 In the general formula (B-2a), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R １ It has a fluorine atom, 'o' represents an integer from 0 to 8.

3. It consists of an acid anhydride and a diamine, The acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formulas (A-2a) to (A-2g). A polyimide resin for low refractive index materials, wherein the diamine is one or more selected from the group consisting of compounds represented by the following general formula (B-3) and compounds represented by the following general formula (B-4). 【Transformation 8】 In the general formulas (A-2a) to (A-2g), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. R ２ Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. 【Chemistry 9】 In the general formula (B-3), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. m represents an integer between 0 and 3. n represents an integer from 0 to 5. o represents an integer from 0 to the maximum number of substituents. R ２ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R ２ This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R ３ ) ２ -, and -SO ２ - Selected from the group consisting of, R ３ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ３ These may bond to each other to form a cycloalkyl group. 【Chemistry 10】 In the general formula (B-4), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and the maximum number of substituents.

4. The above general formula (B-3) is either the following general formula (B-3a) or the following general formula (B-3b), The polyimide resin according to claim 3, wherein the general formula (B-4) is the following general formula (B-4a). 【Chemistry 11】 In the general formula (B-3a), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. 'o' represents an integer between 0 and 4. 【Chemistry 12】 In the general formula (B-3b), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. m represents an integer between 1 and 3. 'o' represents an integer between 0 and the maximum number of substituents. 【Chemistry 13】 In the general formula (B-4a), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R １ It has a fluorine atom, 'o' represents an integer from 0 to 8.

5. The refractive index is 1.57 or less. The polyimide resin according to claim 1 or 3, wherein the coefficient of linear thermal expansion is 50 ppm / K or less.

6. A polyimide resin having the structural unit of the following general formula (1), 【Chemistry 14】 In the above general formula (1), R １ R ａ (CO) ４ The portion represents a tetravalent group derived from a tetravalent tetracarboxylic acid with 2 or more carbon atoms, R ｂ (N) ２ The portion shows a tetravalent group derived from a divalent diamine with two or more carbon atoms. The free volume fraction and average number of neighboring atoms of the amorphous polyimide resin in equilibrium at a temperature of 300 K and a pressure of 1 atm, as calculated by molecular dynamics calculations, satisfy any of the following conditions (1) to (4): (1) The free volume fraction is 0.23 to 0.32, and the average number of neighboring atoms is 3.90 to 4.

60. (2) The free volume fraction is 0.23 to 0.32, the average number of neighboring atoms is 3.90 to 4.60, and it does not contain a trifluoromethyl group. (3) The free volume fraction is 0.24 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not have a trifluoromethyl group. (4) The free volume fraction is 0.28 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not have a trifluoromethyl group. The average number of neighboring atoms is the average number of neighboring atoms per number of atoms constituting the molecular dynamics calculation system, A polyimide resin for low refractive index materials, wherein the number of adjacent atoms is the total number of atom pairs satisfying (a) and (b) below. (a) Atomic pairs that share one side of a Voronoi cell, with each atom as the parent point. (b) Atomic pairs separated by four or more bonds, or atomic pairs between different molecules

7. The free volume fraction and average number of neighboring atoms of the amorphous polyimide resin in equilibrium at a temperature of 300 K and a pressure of 1 atm, as calculated by molecular dynamics calculations, satisfy any of the following conditions (1) to (4): (1) The free volume fraction is 0.23 to 0.32, and the average number of neighboring atoms is 3.90 to 4.

60. (2) The free volume fraction is 0.23 to 0.32, the average number of neighboring atoms is 3.90 to 4.60, and it does not contain a trifluoromethyl group. (3) The free volume fraction is 0.24 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not have a trifluoromethyl group. (4) The free volume fraction is 0.28 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not have a trifluoromethyl group. The average number of neighboring atoms is the average number of neighboring atoms per molecule of the polyimide resin, The average number of neighboring atoms is the average number of neighboring atoms per number of atoms constituting the molecular dynamics calculation system, The polyimide resin according to claim 1 or 3, wherein the number of adjacent atoms is the total number of atom pairs satisfying (a) and (b) below. (a) Atomic pairs that share one side of a Voronoi cell, with each atom as the parent point. (b) Atomic pairs separated by four or more bonds, or atomic pairs between different molecules

8. A composition for low refractive index materials containing the polyimide resin according to any one of claims 1, 3, and 6.

9. A polyimide film for low refractive index materials containing the polyimide resin according to any one of claims 1, 3, and 6.

10. An optical material containing the polyimide resin according to any one of claims 1, 3, and 6.

11. A clad material containing the polyimide resin described in any one of claims 1, 3, and 6.

12. An optical waveguide having a cladding material as described in claim 11.

13. It consists of an acid anhydride and a diamine, The acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formula (A-1a) and compounds represented by the following general formula (A-1b). A polyamic acid for low refractive index materials, wherein the diamine is one or more selected from the group consisting of compounds represented by the following general formula (B-1) and compounds represented by the following general formula (B-2). 【Chemistry 15】 In the above general formula (A-1a), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R １ It has a fluorine atom, m represents an integer between 0 and 3. 【Chemistry 16】 In the general formula (A-1b), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. n represents an integer from 1 to 5. R ２ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ２ These may bond to each other to form a cycloalkyl group. at least one R ２ This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R ３ ) ２ -, and -SO ２ - Selected from the group consisting of, R ３ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ３ These may bond to each other to form a cycloalkyl group. 【Chemistry 17】 In the general formula (B-1), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. m represents an integer between 0 and 3. n represents an integer from 0 to 5. o represents an integer from 0 to the maximum number of substituents. R ２ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ２ These may bond to each other to form a cycloalkyl group. at least one R ２ This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R ３ ) ２ -, and -SO ２ - Selected from the group consisting of, R ３ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ３ These may bond to each other to form a cycloalkyl group. [Chemistry 18] In the general formula (B-2), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R １ It has a fluorine atom, Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and the maximum number of substituents.

14. It consists of an acid anhydride and a diamine, The acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formulas (A-2a) to (A-2g). A polyamic acid for low refractive index materials, wherein the diamine is one or more compounds selected from the group consisting of compounds represented by the following general formula (B-3) and compounds represented by the following general formula (B-4). 【Chemistry 19】 In the general formulas (A-2a) to (A-2g), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. R ２ Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. 【Chemistry 20】 In the general formula (B-3), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. m represents an integer between 0 and 3. n represents an integer from 0 to 5. o represents an integer from 0 to the maximum number of substituents. R ２ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R ２ This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R ３ ) ２ -, and -SO ２ - Selected from the group consisting of, R ３ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ３ These may bond to each other to form a cycloalkyl group. 【Chemistry 21】 In the general formula (B-4), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and the maximum number of substituents.

15. A composition for low refractive index materials containing the polyamic acid and solvent described in claim 13 or 14.

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